Improved handling of large x in ccosh{,f}():
- Handle cases where exp(x) would overflow, but ccosh(x) ~= exp(x) / 2 shouldn't. - Use the ccosh(x) ~= exp(x) / 2 approximation to simplify the calculation when x is large. Similarly for csinh(). Also fixed the return value of csinh(-Inf +- 0i).
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svn2git
2020-12-20 02:59:44 +00:00
svn path=/head/; revision=226599
@ -42,10 +42,12 @@ __FBSDID("$FreeBSD$");
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#include "math_private.h"
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static const double huge = 0x1p1023;
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double complex
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ccosh(double complex z)
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{
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double x, y;
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double x, y, h;
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int32_t hx, hy, ix, iy, lx, ly;
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x = creal(z);
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@ -61,8 +63,23 @@ ccosh(double complex z)
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if (ix < 0x7ff00000 && iy < 0x7ff00000) {
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if ((iy | ly) == 0)
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return (cpack(cosh(x), x * y));
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/* XXX We don't handle |x| > DBL_MAX ln(2) yet. */
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return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
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if (ix < 0x40360000) /* small x: normal case */
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return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
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/* |x| >= 22, so cosh(x) ~= exp(|x|) */
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if (ix < 0x40862e42) {
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/* x < 710: exp(|x|) won't overflow */
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h = exp(fabs(x)) * 0.5;
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return (cpack(h * cos(y), copysign(h, x) * sin(y)));
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} else if (ix < 0x4096bbaa) {
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/* x < 1455: scale to avoid overflow */
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z = __ldexp_cexp(cpack(fabs(x), y), -1);
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return (cpack(creal(z), cimag(z) * copysign(1, x)));
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} else {
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/* x >= 1455: the result always overflows */
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h = huge * x;
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return (cpack(h * h * cos(y), h * sin(y)));
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}
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}
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/*
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@ -36,10 +36,12 @@ __FBSDID("$FreeBSD$");
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#include "math_private.h"
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static const float huge = 0x1p127;
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float complex
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ccoshf(float complex z)
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{
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float x, y;
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float x, y, h;
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int32_t hx, hy, ix, iy;
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x = crealf(z);
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@ -54,8 +56,23 @@ ccoshf(float complex z)
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if (ix < 0x7f800000 && iy < 0x7f800000) {
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if (iy == 0)
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return (cpackf(coshf(x), x * y));
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/* XXX We don't handle |x| > FLT_MAX ln(2) yet. */
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return (cpackf(coshf(x) * cosf(y), sinhf(x) * sinf(y)));
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if (ix < 0x41100000) /* small x: normal case */
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return (cpackf(coshf(x) * cosf(y), sinhf(x) * sinf(y)));
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/* |x| >= 9, so cosh(x) ~= exp(|x|) */
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if (ix < 0x42b17218) {
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/* x < 88.7: expf(|x|) won't overflow */
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h = expf(fabsf(x)) * 0.5f;
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return (cpackf(h * cosf(y), copysignf(h, x) * sinf(y)));
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} else if (ix < 0x4340b1e7) {
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/* x < 192.7: scale to avoid overflow */
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z = __ldexp_cexpf(cpackf(fabsf(x), y), -1);
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return (cpackf(crealf(z), cimagf(z) * copysignf(1, x)));
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} else {
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/* x >= 192.7: the result always overflows */
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h = huge * x;
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return (cpackf(h * h * cosf(y), h * sinf(y)));
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}
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}
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if (ix == 0 && iy >= 0x7f800000)
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@ -42,10 +42,12 @@ __FBSDID("$FreeBSD$");
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#include "math_private.h"
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static const double huge = 0x1p1023;
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double complex
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csinh(double complex z)
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{
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double x, y;
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double x, y, h;
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int32_t hx, hy, ix, iy, lx, ly;
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x = creal(z);
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@ -61,8 +63,23 @@ csinh(double complex z)
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if (ix < 0x7ff00000 && iy < 0x7ff00000) {
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if ((iy | ly) == 0)
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return (cpack(sinh(x), y));
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/* XXX We don't handle |x| > DBL_MAX ln(2) yet. */
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return (cpack(sinh(x) * cos(y), cosh(x) * sin(y)));
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if (ix < 0x40360000) /* small x: normal case */
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return (cpack(sinh(x) * cos(y), cosh(x) * sin(y)));
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/* |x| >= 22, so cosh(x) ~= exp(|x|) */
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if (ix < 0x40862e42) {
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/* x < 710: exp(|x|) won't overflow */
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h = exp(fabs(x)) * 0.5;
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return (cpack(copysign(h, x) * cos(y), h * sin(y)));
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} else if (ix < 0x4096bbaa) {
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/* x < 1455: scale to avoid overflow */
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z = __ldexp_cexp(cpack(fabs(x), y), -1);
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return (cpack(creal(z) * copysign(1, x), cimag(z)));
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} else {
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/* x >= 1455: the result always overflows */
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h = huge * x;
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return (cpack(h * cos(y), h * h * sin(y)));
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}
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}
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/*
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@ -78,13 +95,13 @@ csinh(double complex z)
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return (cpack(copysign(0, x * (y - y)), y - y));
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/*
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* sinh(+-Inf +- I 0) = +-Inf + I (+-)(+-)0.
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* sinh(+-Inf +- I 0) = +-Inf + I +-0.
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*
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* sinh(NaN +- I 0) = d(NaN) + I +-0.
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*/
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if ((iy | ly) == 0 && ix >= 0x7ff00000) {
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if (((hx & 0xfffff) | lx) == 0)
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return (cpack(x, copysign(0, x) * y));
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return (cpack(x, y));
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return (cpack(x, copysign(0, y)));
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}
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@ -36,10 +36,12 @@ __FBSDID("$FreeBSD$");
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#include "math_private.h"
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static const float huge = 0x1p127;
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float complex
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csinhf(float complex z)
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{
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float x, y;
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float x, y, h;
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int32_t hx, hy, ix, iy;
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x = crealf(z);
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@ -54,8 +56,23 @@ csinhf(float complex z)
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if (ix < 0x7f800000 && iy < 0x7f800000) {
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if (iy == 0)
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return (cpackf(sinhf(x), y));
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/* XXX We don't handle |x| > FLT_MAX ln(2) yet. */
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return (cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y)));
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if (ix < 0x41100000) /* small x: normal case */
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return (cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y)));
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/* |x| >= 9, so cosh(x) ~= exp(|x|) */
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if (ix < 0x42b17218) {
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/* x < 88.7: expf(|x|) won't overflow */
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h = expf(fabsf(x)) * 0.5f;
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return (cpackf(copysignf(h, x) * cosf(y), h * sinf(y)));
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} else if (ix < 0x4340b1e7) {
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/* x < 192.7: scale to avoid overflow */
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z = __ldexp_cexpf(cpackf(fabsf(x), y), -1);
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return (cpackf(crealf(z) * copysignf(1, x), cimagf(z)));
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} else {
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/* x >= 192.7: the result always overflows */
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h = huge * x;
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return (cpackf(h * cosf(y), h * h * sinf(y)));
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}
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}
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if (ix == 0 && iy >= 0x7f800000)
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@ -63,7 +80,7 @@ csinhf(float complex z)
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if (iy == 0 && ix >= 0x7f800000) {
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if ((hx & 0x7fffff) == 0)
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return (cpackf(x, copysignf(0, x) * y));
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return (cpackf(x, y));
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return (cpackf(x, copysignf(0, y)));
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}
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